RESUMO
El uso de entornos digitales en línea en la Universidad Jorge Tadeo Lozano ha permitido implementar una base de preguntas con retroalimentación para apoyar al estudiante en el proceso de aprendizaje en la asignatura Pensamiento Matemático. Se desarrolló un proyecto de innovación pedagógica en dos semestres académicos, con el fin de observar si el uso de una base de preguntas con retroalimentación en línea mejora el proceso de apropiación de los conceptos matemáticos de los estudiantes. Las preguntas que conformaron la base se diseñaron siguiendo indicaciones sobre elaboración de preguntas de múltiples opciones con única respuesta; se utilizaron exámenes modelo con los temas vistos en cada uno de los tres momentos en que se divide un periodo académico de la Universidad; dichas evaluaciones formativas fueron puestas a disposición de los estudiantes dos semanas antes de cada evaluación. Debido al carácter del examen -en línea-, con múltiples intentos y accediendo desde cualquier dispositivo, el estudiante podía preparar sus evaluaciones con mayor autonomía y al ritmo que él estableciera. Se realizaron encuestas, entrevistas y grupos focales para identificar algunas características cualitativas que han permitido realizar ajustes y mejoras a la base de preguntas. Los datos obtenidos de cada modelo de examen y los resultados de los estudiantes durante los semestres fueron analizados estadísticamente. Los resultados, tanto cualitativos como cuantitativos, indican que en general, sí hay mejora en el desempeño y apropiación de los conceptos matemáticos en aquellos estudiantes que acceden a los exámenes en línea frente a aquellos que no los usan.
The use of online digital environments at Jorge Tadeo Lozano University has allowed the implementation of a question bank, with feedback, with the purpose of supporting students in their learning process for the subject of Mathematical Thinking; this subject is taught through lectures and workshops that are interrelated and leaded by different professors, one lecture session and two workshop sessions per week. A pedagogical innovation project was developed along two academic periods with the purpose of observing if the use of this online question bank with feedback improved the appropriation of mathematical concepts. The questions that are part of this bank were designed following recommendations for elaborating multiple choice questions with one answer; the selection of distractors for each question was made following conceptual or procedural reasons, which is where most of the difficulties for students are when solving an evaluation on this subject. For each question a detailed description was made, including conceptual aspects and key features such as type of question, question statement, answer choices, reasons for each choice, key information that must be included in feedback (graphics, concepts, solved examples, etc.), cognitive and conceptual domain, level of difficulty, date of elaboration and revision, name of who elaborated the question and name of who reviewed it. Each question was made available on this bank, located at the Virtual Classrooms System at Jorge Tadeo Lozano University (AVATA is the name of this Learning Management System working over Moodle) and corresponding to the Mathematical Thinking course, organized on folders separated by topics and levels of difficulty, according to the available syllabus of the subject. Evaluation models that gathered the topics covered on each of the three segments that form the academic period were used; such formative assessment was made available for students two weeks before each course evaluation. Due to the features of this evaluation, online, with multiple attempts and accessible from multiple devices, students were able to prepare their evaluations with a higher level of autonomy and at the pace, they would establish. Surveys, interviews and focus groups from students and professors that were part of the Mathematical Thinking course were carried out, with the purpose of identifying qualitative features that could eventually lead to adjustments and improvements to the question bank, although not many students participated in these interviews and surveys. Among the qualitative aspects that were highlighted is the fact that students felt comfortable when using this kind of evaluation, as they did not feel the pressure of the results; they also pointed out the role of workshop professors as a motivating element to consult the question bank in order to prepare the evaluations and strengthen mathematical concepts. The data obtained from each evaluation model and the results from students during the academic periods were analyzed statistically, allowing to conclude that there is a significant difference on course grades, both partial and finals, for students who used the evaluation models and students who did not. Results, both qualitative and quantitative, indicated that in general terms there is an improvement in performance for students who access to these online evaluation models compared to students who don't. In order to continue progressing on the work presented here, it is necessary to feed the bank with more questions, considering the aspects indicated from students and professors and also as a way of expanding the possibilities of randomizing the questions as students use the bank. It is also important to carry out statistical analysis to questions, with the purpose of establishing with better precision their levels of difficulty and the levels of difficulty of the evaluation models themselves.
RESUMO
Dados oriundos de investigações recentes em psicologia cognitiva, neuropsicologia e neurociência cognitiva tem permitido um crescente consenso de que as representações numéricas nos adultos e o pensamento matemático culturalmente construído dependem da interação entre o chamado "senso numérico", observado em bebês humanos e em outras espécies animais, e a linguagem. Na pesquisa com bebês, a técnica do "olhar preferencial" tem permitido a descoberta de habilidades sofisticadas em idades precoces, entre elas as de soma e subtração. A neuropsicologia apresenta casos de lesões em áreas do cérebro que causam prejuízos a habilidades específicas, com preservação de outras. E a neurociência cognitiva, por meio de modernos recursos de neuroimagem, tem permitido a localização precisa de áreas cerebrais responsáveis pelo processamento numérico. Todas essas contribuições lançam luzes sobre a natureza da cognição numérica subjacente à matemática. São apresentados e discutidos dados produzidos por pesquisas nas referidas áreas, bem como suas implicações para as teorias clássicas do desenvolvimento cognitivo e do conceito de número, em particular. Discute-se também a visão decorrente sobre a relação entre biologia e cultura, que passam a ser vistas não mais de maneira dicotômica e sim como continuidade uma da outra, bem como implicações pedagógicas e sobre a formação de educadores.
Data from recent research in cognitive psychology, neuropsychology and cognitive neuroscience has allowed a growing consensus that the numerical representations in adults and the culturally constructed mathematical thinking depend on the interaction between the so-called "number sense", observed in human babies and in other animal species, and the language. In research with babies, the technique of "preferential looking" has allowed the discovery of sophisticated skills in early ages, among them those of addiction and subtraction. The neuropsychology presents cases of lesions in areas of the brain that cause damage to specific skills, with preservation of others. And cognitive neuroscience, by means of neuroimaging features modern, has allowed the precise location of brain areas responsible for numeric processing. All these contributions shed light on the nature of numerical cognition underlying mathematics. Data produced by those areas are presented and discussed research, as well as its implications for the classical theory of cognitive development and the concept of number in particular. It discusses also the vision arising on the relationship between biology and culture, which will be seen no more as dichotomous way but as a continuation of each other, as well as pedagogical implications and on the training of educators.
Datos de recientes investigaciones en psicología cognitiva, la neuropsicología y la neurociencia cognitiva han permitido un creciente consenso de que las representaciones numéricas en adultos y el pensamiento matemático culturalmente construido dependen de la interacción entre el llamado "sentido numérico", observados en bebés humanos y otras especies animales y la lengua. En la investigación con los bebés, la técnica de "mirada preferencial" ha permitido el descubrimiento de habilidades sofisticadas en edades tempranas, entre ellos los de suma y resta. La neuropsicología presenta casos de lesiones en áreas del cerebro que causan daño a las habilidades específicas, con la preservación de las demás. Y la neurociencia cognitiva, mediante modernos recursos de neuroimagen, ha permitido la ubicación precisa de las áreas del cerebro responsables por el procesamiento numérico. Todas estas contribuciones arrojan luz sobre la naturaleza de la cognición numérica subyacente a la matemática. Son presentados y discutidos datos de investigación producidos en esas áreas, así como sus implicaciones para la teoría clásica de desarrollo cognitivo y el concepto de número en particular. Se analiza también la visión que surge en la relación entre biología y cultura, que será vista no más como dicotómica sino como una continuación de ambas, así como implicaciones pedagógicas y respecto la formación de los educadores.